A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...

This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist { a j / 2 ? ( ? ? k b ) } , ? Z in L R for which no frame has structure. We first generalize this result by proving approximately Motivated we show imposing very mild decay condition on the Fourier transform of generator certain oversampling N indeed an frame; most importantly, ...

The main purpose of this paper is to find other measurements for constructing optimal duals that minimize the reconstruction errors, when erasures occur. Some known results are investigated with some measurements. Moreover, we investigate extreme points set all 1-erasure by seminorms. Furthermore, examples provided clarification.

Article history: Received 7 June 2011 Revised 7 December 2011 Accepted 30 December 2011 Available online 3 January 2012 Communicated by Karlheinz Gröchenig